Police said Kamil Zieba, 42, was driving on May 21, 2020 when his vehicle struck Jennifer Davies, 69, from Hove.
Mrs Davies, who was attempting to cross the road, suffered serious injuries and died in hospital two days later.
Police said Zieba was charged with causing death by careless driving and at Hove Crown Court he pleaded guilty to the charge on the day he was due to stand trial.
He was found not guilty of causing death by dangerous driving.
His Honour Judge David Rennie sentenced Zieba, of Waterloo Street, Hove, to three years and six months in prison, and disqualified him from driving for four years and nine months.
Police said Zieba was told he would have to take an extended retest should be wish to re-obtain his licence to drive.
The court was shown footage of Zieba’s driving where he repeatedly drove with his hands off the steering wheel, rolled cigarettes, ate and drank, used a mobile phone and checked notes while driving.
Police said it showed his vehicle mounting pavements, sometimes with double yellow lines, reversing from a cul-de-sac into a main road, and other inconsiderate manoeuvres.
The judge said: “Anyone watching that video could be forgiven for thinking that it was only a matter of time before something terrible happened, and it did.
“It was the extremely careless way you chose to drive that day that killed Mrs Davies, and that was completely avoidable.”
Detective Constable Jake Dallaway, from Sussex Police’s Serious Collision Investigation Unit, said: “Zieba’s driving that day put the safety of other road users at risk.
“Drivers should always maintain proper concentration and control of their vehicle, and should always be considerate of other road users while driving.
“By not paying attention to those around him, Zieba caused this tragic collision which was needless and avoidable.”